Let* x *be random
variable with probability density function

A rod of length 2*l*
is broken into two pieces at random. The probability density function of the
shorter of the two pieces is

The mean and variance of the shorter of the two pieces are respectively

Four buses carrying 160 students from the same school arrive
at a football stadium. The buses carry, respectively, 42, 36, 34, and 48
students. One of the students is randomly selected. Let *X *denote the number of students that were on the bus carrying the
randomly selected student.* *One of the
4 bus drivers is also randomly selected. Let *Y* denote the number of students on that bus.